Question

The expected values, variances and standard Deviatiations for two random variables X and Y are given in the following table

Variable | expected value | variance | standard deviation |

X | 20 | 9 | 3 |

Y | 35 | 25 | 5 |

Find the expected value and standard deviation of the following
combinations of the variable X and Y. Round to nearest whole
number.

E(X+10) = ,

StDev(X+10) =

E(2X) = ,

StDev(2X) =

E(3X-2) = ,

StDev(3X-2) =

E(3X +4Y) = ,

StDev(3X+4Y) =

E(X-2Y) = ,

StDev(X-2Y) =

Answer #1

E(X + 10) = E(X) + 10 = 20 + 10 = 30

SD(X + 10) = SD(X) + SD(10) = 3 + 0 = 3

E(2X) = 2 * E(X) = 2 * 20 = 40

SD(2X) = 2 * SD(X) = 2 * 3 = 6

E(3X - 2) = 3 * E(X) - 2 = 3 * 20 - 2 = 58

SD(3X - 2) = 3 * SD(X) - 0 = 3 * 3 = 9

E(3X + 4Y) = 3 * E(X) + 4 * E(Y) = 3 * 20 + 4 * 35 = 200

SD(3X + 4Y) = sqrt(Var(3X + 4Y)) = sqrt(3^{2} * Var(X) +
4^{2} * Var(Y)) = sqrt(9 * 9 + 16 * 25) = 22

E(X - 2Y) = E(X) - 2 * E(Y) = 20 - 2 * 35 = -50

SD(X - 2Y) = sqrt(Var(X - 2Y)) = sqrt(Var(X) + (-2)^{2}
* Var(Y)) = sqrt(9 + 4 * 25) = 10

Let X and Y be independent and normally distributed random
variables with waiting values E (X) = 3, E (Y) = 4 and variances V
(X) = 2 and V (Y) = 3.
a) Determine the expected value and variance for 2X-Y
Waiting value µ = Variance σ2 = σ 2 =
b) Determine the expected value and variance for ln (1 + X
2)
c) Determine the expected value and variance for X / Y

Given independent random variables with means and standard
deviations as shown, find the mean and standard deviation of each
of these variables:
Mean
SD
a) 4X
b) 4Y+3
c) 2X+5Y
X
70
14
d) 5X−4Y
e) X1+X2
Y
10
5
a) Find the mean and standard deviation for the random variable
4X.
E(4X)=_____________
SD(4X)=_______________
(Round to two decimal places as needed.)
b) Find the mean and standard deviation for the random variable
4Y+3.
E(4Y+3)= ________________
SD(4Y+3)= _____________________
(Round to...

Consider independent random variables X and Y , such that X has
mean 2 and standard deviation 4, and Y has mean 1 and standard
deviation 9. Find the mean and standard deviation of the following
random variables. a) 3X b) Y + 6 c) X + Y d) X − Y e) X1 + X2,
where X1, X2 are independent copies of X.

If X, Y are random variables with E(X) = 2, Var(X) = 3, E(Y) =
1, Var(Y) =2, ρX,Y = −0.5
(a) For Z = 3X − 1 find µZ, σZ.
(b) For T = 2X + Y find µT , σT
(c) U = X^3 find approximate values of µU , σU

Let X and Y be jointly distributed random variables with means,
E(X) = 1, E(Y) = 0, variances, Var(X) = 4, Var(Y ) = 5, and
covariance, Cov(X, Y ) = 2.
Let U = 3X-Y +2 and W = 2X + Y . Obtain the following
expectations:
A.) Var(U):
B.) Var(W):
C. Cov(U,W):
ans should be 29, 29, 21 but I need help showing how to
solve.

Suppose X and Y are continuous random variables with joint
density function fX;Y (x; y) = x + y on the square [0; 3] x [0; 3].
Compute E[X], E[Y], E[X2 + Y2], and Cov(3X -
4; 2Y +3).

Let X and Y be independent and identically
distributed random variables with mean μ and variance
σ2. Find the following:
a) E[(X + 2)2]
b) Var(3X + 4)
c) E[(X - Y)2]
d) Cov{(X + Y), (X - Y)}

15.1The probability density function of the X
and Y compound random variables is given below.
X
Y
1
2
3
1
234
225
84
2
180
453
161
3
39
192
157
Accordingly, after finding the possibilities for each value, the
expected value, variance and standard deviation; Interpret the
asymmetry measure (a3) when the 3rd moment (µ3 = 0.0005)
according to the arithmetic mean and the kurtosis measure
(a4) when the 4th moment (µ4 = 0.004) according to the
arithmetic...

Suppose X is a random variable with expected value 260 and
standard deviation 120, and Y is a random variable with expected
value 170 and standard deviation 70. Compute each of the means and
standard deviations indicated below (round off your answers to two
decimal places, if necessary).
E(1.7X)=
SD(1.7X)=
SD(X+Y)=
E(X−Y)=
SD(X−Y)=
Now let Y1 and Y2 be two instances of the random variable YY and
compute the following (again, rounding to two decimal places, if
necessary).
E(Y1+Y2)=
SD(Y1+Y2)=...

Let X ~ N(1,3) and Y~ N(5,7) be two independent random
variables. Find...
Var(X + Y + 32)
Var(X -Y)
Var(2X - 4Y)

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